Homework Help

Find the vertical asymtone: f(x)=`(x-2)/(2x^(2)+3x-2)`

user profile pic

chochkk | eNotes Newbie

Posted October 27, 2013 at 2:56 AM via web

dislike 1 like

Find the vertical asymtone:

f(x)=`(x-2)/(2x^(2)+3x-2)`

Tagged with asymtone, math

2 Answers | Add Yours

user profile pic

flbyrne | (Level 3) Assistant Educator

Posted October 27, 2013 at 3:46 AM (Answer #2)

dislike 1 like

To determine the value(s) of x for which the denominator is 0, solve `2x^2+3x-2=0`. Use the quadratic formula:

`x=(-b+-sqrt(b^2-4ac))/(2a)` for an equation of the form `ax^2+bx+c=0`

Substitute 3 for b, 2 for a and -2 for c.

`x=(-3+-sqrt((3)^2-(4)(2)(-2)))/((2)(2))`

`x=(-3+-sqrt(9+16))/4`

`x=(-3+-5)/4`

`x=-8/4=-2`

`x=2/4=0.5`

The function is undefined for x=-2 and x=0.5, thus x=-2 and x=0.5 are the asymptotes.

user profile pic

Zaca | Student , Undergraduate | Salutatorian

Posted October 27, 2013 at 3:08 AM (Answer #1)

dislike 0 like

Rational functions (functions with a ratio of polynomials) often have vertical asymptotes when the denominator equals zero.

In this case, we can factor the denominator:

`2x^2 + 3x - 2 = (2x-1)(x+2)`

Therefore the denominator equals zero AND we have vertical asymptotes when

`x = 1/2`

`x=-2`

` `   

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes